Random number generator

ABSTRACT

A random number generator comprises a laser for generating photons, an assembly of neutral density filters to attenuate the photons, a photomultiplier tube to detect the occurrence of a fraction of the attenuated photons at a rate of a single photon detected during a set length of time and to detect the occurrence of a single photon during each interval in a series of like time intervals, and a clock and shift register to record a first value for detection of any photons during a selected single time interval in the series of time intervals and to record a second value for detection of no photons during the selected single time interval. The values recorded in the shift register for the series of time intervals are a string of random numbers.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] This invention relates to random number generators and inparticular to random number generators based on detection of quantumphenomena.

[0003] 2. Description of the Related Art

[0004] A random number generator is a device which produces a stream ofrandom numbers or numbers that are nearly random, and not always thesame number. A number in this stream is said to be fully random if ithas no “memory” of what has gone before it. Statistically speaking, itsconditional probability distribution given the past, being independentof its past, equals its unconditional probability distribution.Moreover, it is usually desirable that, for each integer n≧1, theso-called marginal distribution of the nth number in the stream have thesame distribution as the first one. The numbers are then said to bestationary (or have identical distributions). For simplicity, allsequences of truly random numbers are generally to be interpreted asbeing fully random and stationary, and as possibly having equally likelyoccurrences of each number being produced, as the context mighthopefully indicate. It has proved to be very difficult to produce trulyrandom numbers. While people may be capable of producing somewhat randomnumbers by picking numbers out one at a time, they certainly cannot doso fast enough to meet the requirements of modern usage. Therefore, forall practical purposes, machines are used to produce random numbers.

[0005] Most machines and methods heretofore employed for producingrandom numbers are either “deterministic”—they follow a fixed, totallypredictable recipe—or else are still far from truly random. Some devicesproduce nearly truly random numbers, but they are subject to beingskewed by external influences or are very delicate and expensive tomaintain. For many purposes an approximation of randomness has turnedout to be acceptable. For an increasing number of other purposes,something closely approximating true randomness is a necessity.

[0006] Random numbers are most commonly thought of as having securityapplications such as for sending encrypted messages. Random numbers areuseful for security purposes because they create inherentlyunpredictable sequences which cannot be easily duplicated, studiouslyreplicated or discovered by accident. For many lower securityapplications, a random number generator with a reasonable degree ofrandomness will suffice. Higher security applications demand a greaterdegree of true randomness. Another problem that exists with currentrandom number generators, apart from the “level of randomness” of thenumbers that they are able to produce, is that sufficient numbers ofrandom numbers cannot be produced quickly enough for contemporaryapplications. This is significant in security applications wheremessages are encoded with a string of random numbers by adding a bit inthe string to each bit in the message. The result appears to be nonsenseto any recipient until it is decoded by subtracting out the string torecover the message. Ideally, the random number string should be as longas the message itself. In practice, a string—known as a “key”—is usedrepeatedly and it is hoped the string cannot be discovered. The lengthof the key is critically important because each additional random bit inthe string doubles the security level of the cipher. Naturally, ifproduction of sufficient numbers of random numbers were possible andpractical, the level of security enjoyed for encrypted messages wouldincrease exponentially.

[0007] In addition to security applications, random numbers areincreasingly essential for scientific investigations including studiesof physical laws, investigations and constructions of probabilitydistributions, analyses of the performance of mathematical algorithms inprinciple and as applied practically to devices, and notably fordevelopment of artificial intelligence. Random number generators areused in the assessment of the performance of machines to help constructa large variety of representative situations. The sampling thus obtainedprovides feedback which is used to learn more about the process oroperation being studied. As with security applications, problems existregarding the availability of a sufficient volume of random numbers andwith the true randomness of the numbers produced. In a growing number ofareas of scientific inquiry, the ability to produce large numbers ofrandom numbers can be critical. Certain research, such as large-scaleMonte Carlo simulations, requires millions of random numbers to yielduseful information. In sensitive analyses where essentially truerandomness in a sampling is necessary to obtain sound results, anysignificant lack of randomness can unacceptably skew test data andfrustrate the research.

[0008] In part due to the need for large numbers of random numbers, thetechnique of producing “pseudo-random” numbers evolved. Pseudo-randomnumbers are generated using an arithmetical algorithm having an outputof numbers which can pass many statistical tests of randomness. Anotherimportant aspect of arithmetically produced random numbers is that theycan be replicated. This is useful for purposes of testing and analyses,but potentially disastrous for security applications. Whilepseudo-random numbers are statistically random for most applications,and have the application specific advantage of being reproducible, theysuffer from one major flaw—they repeat. For example, a popularpseudo-random number generator is the linear-congruential generator. Thelinear-congruential generator of degree k produces non-negative integersless than some given integer m, where m≧2. At some point, if thegenerator is asked to produce m^(k)+k integers, its last k integers musthave already occurred previously. Since each integer produced by thegenerator is based on the same algorithm, and is therefore dependent onthe previous k integers, this leads into a cycle of repetition that thegenerator cannot escape. In this sense, each pseudo-random numbergenerator has a finite period. The best linear-congruential generatorshave a period exceeding 2 billion. Shift-register algorithms have beenused to greatly extend the period of the generator. Even so, the factremains that, regardless of the length of the period of a pseudo-randomnumber generator, the numbers which are the product of the technique areultimately deterministic and certainly not truly random.

[0009] Most machines are understood to function in the realm ofclassical mechanics according to the physical laws stated by Newton. TheNewtonian world (including the essentially mechanistic world ofMaxwell's equations concerning the behavior of electricity andmagnetism) has at its core, the feature and key premise that if all theinitial conditions (positions, velocities, charges, etc.) of thecomponents of an isolated physical system are known, all of its futurebehavior can be known and predicted. It is therefore ultimatelydeterministic, the generation of truly random numbers or random behaviortherefrom being inherently impossible.

[0010] Moving closer to the observation of quantum phenomena, manydevices have been constructed that take sample measurements of aphysical process (sometimes a macro-scopic, but sometimes a micro-scopicprocess). The measurements are converted into a sequence of elements,each element hopefully having little or no memory (but whether theseelements actually lack memory of any of their predecessors depends bothon the measuring apparatus and the physical process). Production ofrandom numbers from a physical process creates a string of numberswhich, even if not purely random, may seem to be highly so and islargely unrepeatable. This lack of repeatability is a liability inscientific applications, but can be circumvented by recording and/orstoring the actual numbers generated if it is not too costly.Conversely, lack of repeatability itself is not necessarily adisadvantage and may well be an asset in security applications and theinvestigation of artificial intelligence.

[0011] Ostensibly random numbers can be generated using “noise” createdby minor fluctuations in electronic circuits. It is disputed whethersuch electronic noise devices generate true random numbers.Unfortunately, they are often innately slower than pseudo-random numbergenerators making them unsuitable for any application where asubstantial quantity of random numbers is required. Another drawback tonoise based random number generators is that their delicate constructionrequires constant, minute checking to verify that the device has notskewed away from producing true randomness. Electronic noise devices canbecome unstable over time.

[0012] Noise levels are typically affected by fluctuations intemperature and line voltage. Lastly, such devices are very sensitive tosurrounding electro-magnetic fields so that any fluctuation in nearbyelectromagnetic fields can change the output of the device in adeterministic way, thereby skewing the noise away from randomness.

[0013] Because radioactive decay is thought to be a memoryless quantumprocess, independent from atom to atom, random numbers have beenproduced by monitoring the successive decay times of a chunk ofradioactive material. Devices which do so are believed to produceessentially truly random results as opposed to electronic noise devices.However, radioactive materials must be shielded and may therefore beinappropriate for many locations, such as personal computers. As withnoise based devices, radioactive decay devices produce random numbers atunacceptably slow rates.

[0014] Recently there have been advances in the production of randomnumbers using spatially stochastic processes. Using a two-dimensionalposition-sensitive photon-counting detector, the locations of detectedphotoevents on a two-dimensional detector are tracked. A random sequenceof numbers is produced based upon the location (not the time) ofphotoelectrons emitted from a photocathode. While promising, randomnumber generation based on photoevent locations suffers from a number ofvexing problems. The photoevent random number generator is large insize, making it impractical for many applications. It is alsocomplicated to set up and is dependent on position, resolution, speedand dead time.

[0015] Other advances in related fields have focused on the polarizednature of light. Photons have many different polarizations. If a photonis passed at normal incidence through a birefringent crystal, such ascalcite, the photon will pass straight through the crystal, with itspolarization unchanged if it is polarized perpendicular to what isreferred to herein as the optic axis of the crystal. If the photonentering the crystal is already polarized along the optic axis, it willemerge with its polarization unchanged but be shifted to a differentpath than the photons with perpendicular polarization. The photons thathave emerged from the crystal can be detected using detectors, such asphotomultiplier tubes, established in the two respective paths. If aphoton enters the crystal with an axis of polarization, say, half-waybetween the two rectilinear polarization directions, it will berepolarized into either rectilinear polarization direction and followits corresponding path with equal probability. These repolarized photonsare believed to lose all memory of their original diagonal polarization.Relying on the use of two detectors, the diagonally polarized photonshave been utilized by quantum cryptographers to advance a clever schemefor secure exchange of a secret random key that can subsequently be usedto send secret messages. An essential part of the scheme is to thwarteavesdroppers to the message, using the random repolarization ofincident photons having polarizations diagonal to the optic axis of thecrystal. Any measurements by the eavesdropper of such photons wouldrepolarize them and erase the message content inherent in their originalpolarizations.

SUMMARY OF THE INVENTION

[0016] A random number generator is described having a black body sourcefor generating quantum phenomena, a detector for detecting generatedquantum phenomena and a recording system.

BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The present invention will be understood more fully from thedetailed description given below and from the accompanying drawings ofvarious embodiments of the invention, which, however, should not betaken to limit the invention to the specific embodiments, but are forexplanation and understanding only.

[0018]FIG. 1 is a block diagram of one embodiment of a random numbergenerator according to the invention.

[0019]FIG. 2 illustrates one embodiment of a random number generatorhaving a black-body type of source.

[0020]FIG. 3 illustrates one embodiment of a random number generatorthat uses thermionic emission of electrons.

[0021]FIG. 4 illlustates one embodiment of a random number generatorhaving electron emission from a needle.

[0022]FIG. 5 illustrates one embodiment of random number generator thatoperates based on movements of gas molecules.

DETAILED DESCRIPTION

[0023] A random number generator is described. In the followingdescription, numerous details are set forth, such as types of generatorsand detectors, types of quantum phenomena, properties of quantumphenomena, etc. It will be apparent, however, to one skilled in the artthat the present invention may be practiced without these specificdetails. In other instances, well-known structures and devices are shownin block diagram form, rather than in detail, in order to avoidobscuring the present invention.

[0024] This invention utilizes probabilistic features of the creation,absorption, state transitions, and/or responses to energy barriers, anddetection, etc., of quantum phenomena, such as, for instance, photonsand electrons, as well as the molecular movements of gas molecules,together with various scientific and engineering aspects of thedetection, regulating and recording process, to produce what amounts toa (roughly) independent and identically distributed non-constantdetection pulse process or waveform from which random bits or randomnumbers can be extracted during a succession of deterministic or randomlength, adjustable time intervals.

[0025] In one embodiment, a quantum process is set-up which generatesquantum phenomena at an appropriate rate in an essentially predeterminedphysical state or predetermined distribution of states, and the quantumprocess and/or its embodied environment induces these to make atransition into one of two or more subsequent states, according to afixed non-degenerate probability transition distribution. This resultsin transition-based random numbers being generated, which are thendetected by a detector and recorded by a recording device or system. Forsuch an implementation (or in this instance), a mechanism to induce theemission of photons (or electrons) (or to excite electrons by only one,or by two, energy levels, for example) at a suitable rate may be needed.To maintain such a suitable rate, a monitoring and regulatory feedbacksystem may be required.

[0026] In an alternative embodiment, a data analysis technique due toJohn von Neumann in 1951 may be used in conjunction with theaforementioned monitoring and regulatory system. Moreover, for manyapplications, this data analysis technique by itself may be a viablealternative to a full-fledged monitoring and regulatory feed-backsystem.

[0027] The diagonally pre-polarized photons entering the (presumablyrectangular-solid-shaped) calcite crystal constitute one example of amechanism to emit photons. Another would be given by sending singlephotons (or even electrons) through single or multiple tiny apertures(or slits), and setting up two or more detectors, thereby utilizing thephenomena of diffraction and/or interference to generate random numbers.The use of a calcite crystal can be further simplified. To obtain twodistinct possible future photon paths, it is not necessary to rely onthe photon's polarization or the use of a birefringent crystal. All thatis needed is a flat piece of glass (possibly composed of dense flint).Held at an appropriate angle to a photon of wavelength w (and randompolarization orientation), the glass surface will, with roughly equalprobabilities, reflect or refract the photon (and have very lowabsorption probability). In one embodiment, to prevent interferingreflections from the back surface of the glass, the original surfacecould be part of the hypotenuse of a suitable right-angled prism.

[0028] Each of the above embodiments can be further simplified. Notefirst, that virtually every combined detection, monitoring and recordingsystem requires implicit or explicit use of a clock. Thereby, if oneknows the rate at which photons are striking either the crystal, theapertures, and/or the flat glass surface, the clock mechanism itselfwill permit one to drop all but one detector. The lone remainingdetector is placed along only one of the primary future possible pathsof the photon. Random bits can then be produced based on whether or notthe detector received either at least one registered pulse or noregistered pulse during each of a succession of distinct, suitablyconstructed time intervals. (Higher random bit rates can be achievedwhen there is more precision in the measurement system and quantitiesmeasured. For example, suppose that the time is measured from the startof a detection interval until the time a registered detection pulse isfirst received. Let T₁, T₂, denote the successive elapsed times afterthe start of such (T1-like) time intervals. If the T_(j) are nearlyindependent and identically distributed as exponential or geometricrandom variables with slowly varying parameter, the random variables$X_{j} = \frac{T_{2j}}{T_{j - 1} + T_{2j}}$

[0029] will be approximately independent and uniformly distributed onthe unit interval in the ideal analog case and on the n−1 points$\left\{ {\frac{1}{n}{,\quad}\quad \frac{2}{n}{{,\quad}\quad.\quad.\quad.\quad \frac{n - 1}{n}}} \right\},$

[0030] when the time interval T_(2j−1)+T_(2j) has been digitized andsplit into n subintervals of equal length.) Since the randomizationintroduced above at the interface of the air and the crystal, air andglass, or at the apertures, is already present in the unpredictablecharacter of the detection process itself (and probably also in mostgeneration and attenuation procedures one might employ), the crystal,aperture(s), and flat glass may be dropped in favor of a more directtime-based procedure, relying primarily on the generation and detectionprocesses themselves.

[0031] Time-based methods (and composites of the two methods) may beused to generate random numbers using quantum phenomena. To understandhow, note that the time required for a quantum process to make atransition out of its current (initial) state is usually believed orassumed to be an exponentially distributed random variable having somefixed parameter depending only on this current state. Given this state,this random exit time is further assumed to be independent of the past.

[0032] Independence is usually further assumed concerning what ishappening at separate locations. Thus (as a gedanken experiment), if onehas a collection of n hydrogen atoms, each with its electron in anexcited state k energy levels above the ground state, each electronwould be assumed to wait a random time (T_(kj) for the j^(th) electron)until it made a transition out of that state.

[0033] When making a transition, it is assumed that the electron wouldmove to the i^(th) energy level with some probability p_(ki), wherep_(ki)≧0, p_(ki)=0 for i≧k, and p_(k0)+p_(k1)+ . . . +p_(k,k−1)=1. It isassumed that for each k greater than or equal to 1, T_(k1), T_(k2), . .. , T_(kn) are independent exponentially distributed random variables,each equipped with the same fixed parameter λ_(k>)0. For simplicity,take k=1. In this case, every transition out of the first energy levelresults in moving to the ground state (the zero^(th) energy level)together with the simultaneous release of a photon of fixedcharacteristic wavelength.

[0034] Although the above assumes that an electron jumps to a lowerlevel when it moves out of any level, it may also move to a higherenergy level as well.

[0035] Hence, by detecting a photon of such wavelength, electrontransition times may be monitored and nearly detected. In fact, listingthe transition times T_(k1), T_(k2), . . . , T_(kn) in order fromsmallest (i.e., the temporally first occurring time) to largest (i.e.,the temporally last occurring time) produces the first n points in aconstant rate Poisson process with rate determined entirely by λ_(k) andn. So if each of the n photons so produced is independently detectedwith constant probability p>0 of detection, then the stream of detectionpulses is also distributed as the first (roughly) np points of aconstant rate Poisson process. From this detection pulse process, randomnumbers can be constructed.

[0036] A further method of generating random numbers includes sending,according to a roughly constant rate Poisson process, particles of someenergy A or narrow distribution of such energies toward a quantummechanical energy barrier of magnitude B>A and then counting thoseparticles that manage to tunnel through the barrier. Yet other methodscould be based on diffraction through a microscopic rectangular array ofbarrier pillars, or on circular polarization, possibly using chiralmolecules. A random number generator according to one embodimentcomprises a generator of quantum phenomena, an attenuator of the quantumphenomena, a detector, and a recording system. An example of such asystem is shown in FIG. 1. These elements may be combined together witha direct current, or suitably high-frequency alternating current,controllable power supply, monitoring and regulatory system, and theinput phenomena may possibly be gated. The recording system may include,but is not limited to, a flip flop, one or more mechanisms to read andreset the flip flop, one or two clocks, and a shift register.

[0037] In one embodiment, a laser generates quantum phenomena byproducing photons. It should be recognized that other quantum phenomenongenerators could be used such as, for example, a cathode emitter forelectrons. Photons generated by the laser are directed towards anattenuator to reduce the quantity of photons exiting the attenuator to adesired average number detected per second during an established timeinterval. This number may be inferred from data such as but not limitedto: i. the rate at which the quantum phenomena are produced by thegenerator; ii. the rate of attenuation produced by the attenuator;and/or iii. the proportion of time that single (isolated or individual)quantum phenomena which enter the detector produce a registered pulse.The attenuator may be used to avoid exceeding either the capacity of thedetector or the recording system, in addition to preventing the effectof the deterministic law of large numbers from overwhelming the inherentrandomness of the successive individual quantum events. Hence there aremany embodiments in which no attenuator is required.

[0038] The power of the laser and the reduction ability of theattenuator are coordinated to produce a desired average number x>0 ofdistinct (e.g., registered) detector (or detection) pulses of a suitablepredetermined constrained amplitude and duration during a preliminaryestablished (e.g., large) time interval. Even though the number ofphotons actually emitted is indeterminable, the number of registereddetection pulses may be determined. In one embodiment, to generaterandom numbers from the registered pulses, the time between successivepulses is approximately an exponentially distributed random variablewith essentially constant parameter and essentially independent frominstance to instance. If the parameter is slowly changing (for examplein response to the generator using a driving alternating current orpulsating direct current or due to slow variations in photon output dueto heating effects, power line voltage fluctuations, etc.), it ispossible to largely correct for this defect by a data analysis techniquedue to John von Neumann in 1951. In one embodiment, in which a constant,but controllable, DC current generator is included, a monitoring andregulatory feedback system may also be employed to ensure that a stabledetection rate is maintained.

[0039] A detector receives the photons from the attenuator. In oneembodiment, the detector is capable of recognizing a certain minimumthreshold number of photons with a certain non-negligible probability,outputting a pulse of a certain minimum or constrained amplitude and acertain constrained duration. Such a pulse may be referred to herein asa registered pulse, a registered detector pulse, a registered detection,or a registered photon (quantum) event, etc. In one embodiment, thedetector is capable of recognizing a single photon by outputting aregistered pulse with a certain fixed non-negligible probability, whichmay depend on the wavelength of the photon.

[0040] If the threshold number is set too high (for example 10,000 ormore), however, then relatively small percentage changes in photonoutput by the laser or other photon source may result in either everysample for a relatively extended time period exceeding the threshold andso generating a long string of ones (where a 1 indicates a sampleexceeding the threshold), or else every sample in a relatively extendedtime period falling below the threshold and so generating a long stringof zeroes (where a 0 indicates a sample not exceeding the threshold).This phenomena occurs whenever the change in photon output from itsintended rate exceeds and tends to remain, say, plus (or minus) at leastthree to five or so times the square root of the threshold level,assuming that the detector's ability to detect a threshold is accurateup to (roughly) a plus or minus the square root of the threshold. Whilethis difficulty is somewhat correctable via the von Neumann technique,the effect of having to employ it is to lose long bit strings whilewaiting for the device to somehow return to production of the criticalnumber of photons per detection interval.

[0041] In one embodiment in which the duration of a registered pulse canbe somewhat ignored, the electrical signals from the detector are usedduring a period of time T1 to (potentially) set a binary flip flop (orother recording system or mechanism) to the one state. The probabilitythat the flip flop will be in the one state at the end of this T1 periodis roughly a function of the ratio of T1 to the average time intervalbetween registered pulses. For one case in which the registered detectorpulses constitute a stationary independent (approximately Poisson)process, there is some real value of T1 which will make this probabilityequal to ½ (50%). To determine and communicate the state of the flipflop at time T1, additional time is typically needed. Thus, at some timeincrement T2 after the end of the period T1, the state of the flip flopcan be determined. This state is used to set the next bit in the bitstream being generated, a one producing a one and a zero producing azero (in one embodiment). Then the flip flop is reset to, for example,the zero state. After an additional time T3 following the T2 period, anew T1 period is started. The period T3 is used to allow time for theflip flop to be reset to the same (zero) state at the start of every T1time period and to allow time for any pulses generated during the T1time period to have dissipated with high probability. Thus, in such anembodiment, the total time required to generate one bit in the randombinary bit sequence is T1+T2+T3.

[0042] Therefore, during each cycle period (of length T1+T2+T3), a valueof zero is recorded if no registered pulses have occurred during (orfrom) the T1 portion of the cycle, and a value of one is recorded if oneor more registered pulses have occurred.

[0043] If the duration of a detection pulse is too long relative to theT1 time interval to be ignored, neighboring bits may become dependent,showing bursts of ones. However, as long as the underlying photonemission process has certain independence properties, the independenceof neighboring bits can be reestablished in convenient fashion. Forexample, when the photon (or quantum event) emission times constitute a(constant rate) Poisson process, independence from all previouslygenerated bits may be achieved as soon as both the detector output pulsewaveform and the waveform in the transmission channel into which theelectrical detector signals from the new T1 time period will bedeposited (as will be discussed in somewhat more detail below) drop totheir respective “resting levels”. Hence, by waiting a sufficiently longtime after the end of the current T1 time period, it is permissible(with high probability) to begin the next one. In another embodiment,the detector pulse waveform amplitude and the amplitude of the relevantassociated detector signal deposition channel could be checked at thebeginning of each T1 time period, dropping the bit produced during thatT1+T2+T3 cycle period if either amplitude exceeded its own relevantexperimentally determined threshold, and retaining it otherwise. Toincrease the bit rate, one could continuously, or very frequently,monitor the detector output waveform and the waveform of the relevanttemporally associated detector signal deposition channel, and begin thenext T1 time period at the first feasible time after the end of thecurrent T1+T2+T3 cycle such that each waveform is at its own respective“resting level”.

[0044] The random numbers (bits) are directed to the shift register (ofone embodiment of the recording system) as they are produced. For onecase, in which the successive registered detector pulses are wellapproximated by a constant rate Poisson process, the probability of noreceived registered pulse during a time interval of length L is roughlyexp (−Lλ), where λ is the Poisson arrival rate. This quantity equals ½when L=(ln 2)/λ. Here exp (x) is the usual exponential function of x,whose value is given by the infinite series 1+x+x2/2!+ . . . .Analogously, ln2 denotes the natural (Naperian) logarithm of 2, whosevalue is given by the infinite series 1−½+⅓−¼ . . . . Moreover, theapproximate probability of one or more registered pulses occurringduring such an interval L is 1−exp(−Lλ), which is also one-half whenL=(ln2)/λ;. For this reason, in one embodiment, the length of the T1time period is set approximately equal to (ln2)/λ, giving anapproximately independent, identically distributed (i.i.d.) stream ofones and zeroes of roughly a 50% chance of one and a 50% chance of zero.If so desired, these bits can be made more nearly purely random andequi-probable by passing to a subsequence.

[0045] When a photomultiplier tube (PMT) or electron multiplier tube(EMT) is used to detect quantum events, a registered detection pulse ofa photon or an electron will typically result in about 10⁶ or 10⁷electrons hitting the final dynode plate in the PMT (or EMT, etc.). Thisusually is an insufficient amount of charge to be directly recordedwithout further processing. Common photon counting procedures (which areclose to typical needs) process the pulses outputted by the PMT (orother detector) by putting the pulse through a pre-amplifier (e.g., awide band amplifier) which converts pulses to voltages. Thereafter, amain amplifier receives and amplifies the voltages. Then a discriminator(and/or comparator) compares the input voltage pulses with a presetreference voltage (threshold level) and eliminates pulses withamplitudes lower than this value. The output of the discriminator issent to a pulse shaper and then to a counter which counts the pulses.The counter may be equipped with a gate circuit, which allowsmeasurement at different timings and intervals. In addition, in oneembodiment, to reduce false photon counts due to “ringing”, a very shortwiring or a coaxial cable (to match its impedance) may be used from thePMT or other detector. Such a solution is well known to those skilled inthe practice of the art.

[0046] Some or all of these more specific electronic systems (andpossibly others as well) may be employed to transform the output of thePMT or other detector into the desired binary bits, together with aFirst In, First Out (FIFO) buffering system and the aforementioned shiftregister (which shifts at the rate of once every T1+T2+T3 seconds or incorrespondence with the completion of a bit producing T1+T2+T3 cycleperiod). The flip-flop device mentioned above is part of this successionof electronic devices in many embodiments.

[0047] If there is a desire or need to produce random bits as rapidly aspossible, it may be necessary or desirable to send the electronicsignals from the PMT (or other detector) and multiplex or distributethem sequentially into one of n channels, each of which is equipped withthe electronics, such as described above, to independently convert thePMT output into an enhanced pulse which may be counted. The results ofthe conversion may then be demultiplexed and then sent to the shiftregister to create an output (random) bit. The multiplexor attainsgreater bit generation rates by overcoming the problems due to pulsewidth spread as the signal is enhanced. To understand how, suppose thatonce a pulse comes from the PMT, a total time of Tp seconds is requiredto process it from pre-amplification through to bit generation andresetting. When this time exceeds the T1+T2+T3 time period, or rather islarge relative to the T1 time period, damaging pulse pileups may occur.To prevent this, some number n of disjoint and/or distinct amplificationchannels may be used, which can operate in parallel and which can be setin motion one-by-one in a succession (for instance, by use of amultiplexor) and which wraps around after the n^(th) channel has beenused.

[0048] Let Δ_(s) denote the time required by the multiplexor to shiftfrom one channel to the next. At the completion of each T1 detectiontime period, the multiplexor shifts, sending the electrical signals fromthe PMT (or other detector) into the next available channel. Thisrequires Δ_(s) time units to set up, after which a new T1 time period isbegun (or eventually cleared to begin).

[0049] Thus, as long as n times T1+Δ_(s) equals or exceeds T1+Tp and theelectrical current in the first channel (and hence in each of the otherchannels in succession) can re-equilibriate within n times Δ_(s) plusn−1 times T1 seconds (time units), the bit generation can be performedsuccessfully.

[0050] A further increase in the rate at which random bits can beproduced can be obtained if one uses a position-sensitive PMT, havinggrid and fine-mesh dynode plates designed for this purpose, keepingtrack not only of whether and when a registered pulse occurred, but onwhat region of the final plate it was primarily located.

[0051] A random number generator is generally depicted in FIG. 1. In oneembodiment, the device 10 comprises a laser 12 (or other quantumphenomena generator) to generate photons. The laser 12 produces photonsaccording to a Poisson process having nearly constant or sufficientlyslowly or sufficiently rapidly varying (roughly cyclical) Poisson raterelative to a certain specified or adjusted time period(s) associatedwith the detection and recording process. In particular, if the Poissonrate is non-constant, it varies sufficiently slowly relative to both thetime periods T1 and T1+T2+T3, or sufficiently rapidly relative to thetime period T1.

[0052] Note that photons are a convenient quantum media and can beeasily produced. Any common light source may be used to generatephotons, but a laser or tungsten filament with a direct current powersource (Tungsten is a heat conductor and can be heated by passing anelectrical current through it, in one embodiment.) is more likely toproduce a constant, even flow of photons. An alternative embodimentcould use any source of any kind of photons with a frequency high enoughto be detected by the photon detector used. Such a source wouldpreferably operate so that the registered detection pulses during the T1detection intervals occur as a roughly Poisson process with nearlyconstant or sufficiently slowly or rapidly varying roughly cyclicalrate. Most lasers produce a great many photons. Other photon generatorscould include, for example, an LED, or a source of x-rays satisfyingPoisson process and rate conditions, or possibly a scintillation device.Single photons can be produced using a spectrometer or an ultra-highfrequency helium-neon laser. (There may be some unwanted periodicity inthe photon output of the latter photon source. Nevertheless, if thecycle time of the generator is short enough relative to the T1 timeperiod associated with the detection process, or else is essentiallyperfectly synchronous with it, the registered detection pulses duringthe T1 time interval will constitute a (roughly) i.i.d. random processand thereby be capable of generating high quality random bits).

[0053] Also, even if these latter two devices produce a single photonvirtually on demand (and so, by the way, require no attenuation), therandomness of the quantum detection process will convert such anostensibly deterministic emission scheme into a random registereddetection pulse process. To produce i.i.d. random bits, the emissiontimes are synchronized with the T1 and T1+T2+T3 time periods andregulated so that virtually the same number no of emissions (or, rather,emission arrivals) occur during each successive T1 time period. If thedetector then produces a registered detection pulse with probability P₀from receipt of a single photon, the probability of generating a zerobit by this embodiment is (essentially) (1−P₀)^(n) ^(₀) . Ideally, sucha P₀ should be coordinated with no so that this probability equals(roughly) one-half.

[0054] It should be understood that the random number generator alsocould be constructed using a generator of other kinds of quantumphenomena. For example, any source of electrons, such as cathodeemissions of electrons, could be used. Again, such a source wouldpreferably operate such that the detection pulses that are registeredsatisfy various Poisson process and rate conditions. An alternativeembodiment comprises a cathode emitter for generation of free electrons.In one embodiment, a one milliwatt helium-neon laser 12 is used togenerate approximately 3×10¹⁵ photons every second. The laser 12 has theadditional advantage of not being acutely sensitive to minutefluctuations in surrounding electromagnetic fields. Despite any suchfluctuations, the laser will probably generate a satisfactorily uniformoutput of photons.

[0055] To utilize the random occurrences of photons, the number ofphotons produced by this laser is attenuated. In another embodiment, aspectrometer is used to generate single photons, and no attenuation maybe necessary. But, in one embodiment, photons are attenuated using anassembly of neutral density filters 14. Given the generation ofapproximately 3×10¹⁵ photons by the laser 12, neutral density filters 14with a combined optical density of 10.3 achieve an attenuation factor of5×10⁻¹¹ to reduce the photon output to an average number of 150,000photons every second with a mean distance between photons of 2 km. Thisattenuation factor is achieved via reflection and absorption, with theoptical density D of the neutral density filters 14 defined as$D = {{\log_{10}\left( \frac{I_{o}}{I_{\tau}} \right)},}$

[0056] with I_(o) representing the incident intensity of the light whileIr represents the transmitted intensity of the light. The attenuationfactor is reached in one embodiment using an assembly of two neutraldensity filters each having an optical density of 5.0 and a third filterhaving an optical density of 0.3, such as are available from ReynardCorporation of San Clemente, Calif. Any other combination of neutraldensity filters achieving the requisite attenuation could be used,provided that multiple reflections are not permitted to occur (or areinconsequential) between the individual filters. For example, in anotherembodiment, five neutral density filters each having an optical densityof 2.0 are used in combination with a neutral density filter having a0.3 density. Any optical filters capable of attenuating the photons fromthe generator to the requisite degree could be used. In one embodiment,multiple plate polarizers achieve the same attenuation factor asachieved using the neutral density filters. In fact, multiple platepolarizers can be used to greatly vary the degree of attenuation.Because their rate of attenuation varies with orientation, multipleplate polarizing filters, used alone or in conjunction with neutraldensity filters, can be used to provide a highly adjustable degree ofattenuation (via rotation) not available by use of neutral densityfilters alone.

[0057] Highly adjustable attenuation may also be achieved by use of adarkened liquid or gas located between the photon generator and thedetector, assuming that the light source is secured to a trackmechanism, in one embodiment, so that its distance from the detector canbe adjusted by some suitable mechanism (e.g., knob, dial, etc.). Theliquid or gas is sealed off from these devices as well as from theexternal environment. Moreover, to prevent damage should leakage occur,the liquid should be chosen to be something which evaporates at ambienttemperature (such as alcohol impregnated with ink or an ink-likesubstance, or even water in which potassium permanganate and possiblyother substances are dissolved).

[0058] Letting aw denote the length of liquid or gas between photongenerator and detector which can achieve a reduction in photons enteringthe detector by a factor of 10, for a given wavelength of light w, avolume of such darkened liquid stretching out da_(w) units between thegenerator and the detector gives an attenuation factor of 10^(d) forwavelength w.

[0059] Varying the distance between the light source and the detectorvaries the length of liquid between the two and hence the degree ofattenuation achieved. Controlling entry to the detector (and/or exitfrom the photon or quantum event generator) by an abutting pin-holeaperture can also provide much attenuation, possibly in conjunction withone or more successive convex mirrors (or even darkened sphericalsurfaces) of variable in between distances and suitably arrangedlight-blocking panels. In the embodiment wherein free electrons aregenerated, a thin metal plate having applied to it a constant source ofelectric charge in a vacuumed housing can attenuate the electrons.

[0060] As shown in FIG. 1, the photons transmitted from the neutraldensity filters 14 are detected using a photomultiplier tube 16 such asmanufactured by Hamamatsu Corporation of San Jose, Calif. In oneembodiment, the photons generated by the laser 12 have a wavelength of632.8 nanometers. The photomultiplier tube 16 is capable of detectingphotons of that specific wavelength. In one embodiment, thephotomultiplier tube 16 is able to detect a single photon withnon-negligible probability. The photomultiplier tube has a detectionefficiency of 0.2. It is assumed that this means (or else the number 0.2is replaced by the number which does have this meaning) that when anisolated single photon from the given laser enters the detector, it hasprobability 0.2 of generating a registered detection pulse. It can beappreciated that any photo detector capable of reliably detecting asingle photon could be employed in place of a photomultiplier tube,bearing in mind that different photo detectors will have differentlevels of detection efficiency. In an alternative embodiment, anavalanche photo diode may be used instead of the photomultiplier tube16. In other embodiments, charge-coupled devices might be employed todetect low photon levels. In one embodiment based on generation of freeelectrons, an electron multiplier tube acts as the detector.

[0061] Treating the neutral density filters 14 quantum mechanically, onecan imagine that each photon emitted by the laser 12 and directed towardthe neutral density filters 14 behaves independently of any priorphotons and each has an identical positive probability P_(f) (assumingthat all of the photons have the same wavelength) of passing through thefilters 14 and emerging on the other side, from whence it enters thephotomultiplier tube 16 (or other detector). Note that P_(f) may dependupon the wavelength of the photon. The detector itself acts as anotherre-sampler and re-randomizer, detecting each photon (or quantum event)it receives by outputting a registered detection pulse with probabilityP_(d) (which could vary with the wavelength of the photon),independently of the past (assuming the detector has had time tore-equilibrate) and of the attenuator, etc. Hence a photon emitted bythe laser 12 generates a registered detection pulse with probabilityP_(f)P_(d). If n photons are emitted by the laser 12 during a timeinterval of length L, the probability that these do not result in aregistered pulse is (1−P_(f)P_(d))n. Letting ln (x) denote the naturallogarithm of x, the n which makes this probability nearly ½ is obtainedby setting n=−1n2/ln(1−P_(f)P_(d)), which is approximately1n2/(P_(f)P_(d)+(P_(f)P_(d))²/2). In one embodiment, P_(f) isapproximately 5×10⁻¹¹ (assuming that P_(d) is approximately 0.2). (Ofcourse one could adjust P_(f) to compensate in case P_(d) had adifferent actual value.) Since 1n2 is about 0.7, it follows that if theT1 time interval may be set so that during such period the laser emitsabout n=7×10¹⁰ photons, then the probability of no registered detectionpulse during such time period is approximately ½. In one embodiment, thelaser 12 emits about 3×10¹⁵ photons per second. Hence the T1 timeinterval should last about 7/3×10⁻⁵ seconds, for the probability of noregistered detection, plus perhaps an additional twenty nanoseconds orso (and it could be much less in some embodiments) for the duration of aregistered pulse, because the probability of no registered pulse duringa T1+T2+T3 detection and recording cycle should be approximately ½(although this could be modified should other probabilities be desired).It should be pointed out that the nature of the randomness within the T1time interval as well as between successive T1 intervals dependsprimarily on the emission stream of photons from the laser (or whateverprocess was responsible for generating the photons or other quantumsource), and secondarily upon the attenuation and detection processes.

[0062] As generally shown in FIG. 1, at the beginning of a detection andrecording cycle, the flip flop 18 is to be found in the zero state. Upona registered detection of a photon or multiple photons during theinitial T1 time period, the photomultiplier tube 16 or other detectionapparatus creates a suitable electronic pulse which is transmitted tothe flip flop 18, changing its state to one if it was zero, and leavingit in the one state otherwise.

[0063] Regardless of whether a registered pulse has occurred, the flipflop 18 is read at the end of a T1 time interval (as measured by a firstclock) and its state transmitted to a shift register 20. The flip flop18 is then reset back to the zero state and after the passage of a totalelapsed time of T1+T2+T3 time units since the start of the currentdetection and recording cycle (as measured by a second clock) anothersuch cycle is begun, starting with a T1 detection period. The first andsecond clocks may be the same or different, but synchronized. In oneembodiment, the second clock tracks the successive T1+T2+T3 timeintervals. The shift register 20 shifts every T1+T2+T3 time units. Inother embodiments where there is pulse amplitude monitoring of the PMToutput waveform and/or the associated detector deposition channel(s),the rate and time at which the bit shift register shifts is alteredaccordingly, or else the bits produced undergo a correspondingmodification. In one embodiment, T1 is about (7/3)×10⁻⁵ seconds. It iswell known how to measure much shorter temporal intervals, such asnanoseconds (1×10⁻⁹ seconds). It is expected that the T2+T3 timeinterval be sufficiently longer than the fall time of the detector, aswell as the duration of a registered pulse. The value of T2 and T3depend upon the electronic equipment but are presumed to (typically) beof much shorter total duration than T1 (though this is not essential).Hence, in this case, the shift register 20 collects a sequence of zeroesand ones at the rate of roughly 43,000 per second. If, in addition, thephotons emitted by the laser 12 constitute a (roughly) constant ratePoisson process, then, also assuming that the duration of a registeredpulse is of lower order than T1, the registered detection pulses willalso be (very closely approximated by) a constant rate Poisson process,in which case, (whatever the T1 time period) the output stream of zeroesand ones will nearly be an independent and identically distributedsequence of random variables. Then, if the T1 time period is setproperly (as previously discussed), the ones and zeroes produced by theshift register will be (roughly) equally likely, each having probability½ of occurrence. Moreover, the T1 time period, as well as the photonoutput of the laser 12 (or other generator of photons or quantumphenomena), the attenuation factor of the neutral density filters 14 (orother attenuation assembly), and/or the detection efficiency of thephotomultiplier tube 16 (or other detector), can be adjusted to producevirtually any other desired proportion (i.e., probability) of ones.

[0064] Frequently, there is a lack of constancy in the photon (orquantum) emission rate of the laser (or other generator of quantumphenomena) caused by the periodicity of an alternating current powersource and resulting in a periodic ripple in the number of photonsproduced (of period possibly equal to one-half the cycle time of thealternating current). For this reason, a direct current or sufficientlyhigh frequency power source might be used. This could also be augmentedand compensated for by von Neumann's data analysis technique (at thecost of a factor of about four in the bit rate whenever the proportionof ones is initially between 40% and 60%).

[0065] To properly analyze the degree of randomness of the bits producedby, say, the cycling pair of time intervals T1 and T1+T2+T3 when used inconjunction with a flip flop bit generation device, let us let N(t)denote the random (presumably, and for simplicity and ease of analysis)Poisson process which represents the successive emission times ofphotons (or quantum events) from the photon source which actually enterthe detector and generate a registered pulse. Thus, letting τ₀=0,τ₁=inf{t>0: N(t)=1}

[0066] and, more generally, for each k1, letting τ_(k)=inf {t>0:N(t)=k}, then τ_(k)−τ_(k−1)

[0067] is the elapsed time between the k−1^(st) and k^(th) such photonemission. Unfortunately, the detection system does not preserve theseemission times, the reason for this being that the transit time from thephoton source to the first stage of the detector is not quitedeterministic, and secondly, but far more importantly, a photon arrivalwhich is sensed will generate a whole cascading barrage of electrons onthe final plate (of the photomultiplier tube, for example) and thesewill occur at a variety of times, thereby smearing out the informationconcerning the generating photon's actual emission time. Let (F_(k),L_(k)) denote respectively, the elapsed time from the emission of thek^(th) detected photon until the first generated electron hits the lastplate, and until the last generated electron hits the last plate. Then,ignoring dark current, the generation of a registered detection pulsewill be based on what happens during the time interval [τ_(k)+F_(k),τ_(k)+L_(k)]. It is conceivable that two or more of these intervalswould intersect. (This problem is further compounded and of increasedlikelihood due to the time it takes for such electrical charges todissipate.) Indeed, this will happen frequently unless E(L₁-F₁), theexpected value of L₁-F₁ (and so of L_(k)-F_(k)), is of lower order thanE τ₁, the expectation of τ₁. Such an overlap of intervals will not onlymake pulses difficult to separate, it may cause the affected (nearby)bits to be dependent.

[0068] Therefore, if E(L₁-F₁) is of the same order of magnitude as E τ₁or larger, to generate a stream of independent bits, it would seemnecessary to do at least one of two equivalent things: either increasethe duration of the T2+T3 time period so that E(L₁-F₁) is sufficientlysmaller, or replace the originally generated bit stream Y₁, Y₂, . . ..by the bit substream Y_(m), Y_(2m), Y_(3m), . . . for sufficientlylarge m. (Note: there is nothing that can be done with the T1 timeperiod because T1 is fixed at a value of roughly ln2 times E τ₁ possiblyplus a certain (to be chosen) fraction of the average duration of aregistered pulse). Alternatively, the pulse amplitude of the detector(and possibly also, at the same or somewhat later time, the prospectivepulse deposition channel) could be monitored at the time of or justprior to the potential beginning of a T1 time interval to determinewhether the pulse height (pulse amplitude) was at a “resting level”, asdiscussed above. This latter approach would presumably provide a veryreliable method of generating independent bits.

[0069] Whenever the PMT or other detector puts out signals that must befurther amplified and/or modified to produce bits, the detector pulsewaveform may be further smeared out. The buffering, multiplexing, and/orpulse amplitude monitoring system proposed is designed to maintain theintegrity (separation and unicity) of registered detection pulses and toinhibit or prevent amplified versions of virtually any pulse waveformsfrom the detector from overlapping and piling up, thereby inducing falsereadings.

[0070] Feedback System for Regulating the Power Supply

[0071] Moreover, despite all efforts to prevent it, there may be someinevitable variation in photon (quantum) emission rate or even detectionrate from any light (quantum) source or detector due to power linevoltage fluctuation, heat buildup, electrical contact fluctuation,aging, photomultiplier tube dynode plate voltage instabilities, thermalchanges in the environment, etc. However, the registered detectionpulses themselves (of single photon or single quantum events, in mostembodiments) can be used to monitor the variations in photon (quantum)emission and/or registered detection rate and thereby keep thingsproperly regulated, maintaining a generally stable flow of registeredphoton (quantum event) detections without significantly impinging on thecapability of the system to produce nearly truly random numbers (bits).One simple way of doing this is to fix an integer n_(*) (sayn_(*)=40,000 in one embodiment) and fractions 0<γ₀<γ₁<1 (say y₀=0.49 andγ₁=0.51, in one embodiment) and let W_(n) denote the number of onesamong the last n_(*) bits produced by the device (such as by the flipflop and shift register) (before any von Neumann data manipulation ofthe bits or the like) up to and including the n^(th) bit. IfW_(n)≦γ₀n_(*), marginally increase the power to the photon (quantum)source. If W_(n)≧γ₁n_(*), marginally decrease the power. Otherwise, thepower should be left alone. Moreover, if the power has just beenadjusted, it should not be readjusted until a least some reasonablefraction of n_(*) additional bits have been produced. For improvedreliability and performance, the fractions should be chosen so thatγ₀<P_(*)<γ₁, where P_(*) is the desired proportion of ones in the bitstream, and also, γ₁−P_(*) and P_(*)−γ₀ should probably be about equal,and {square root}{square root over (n)}_(*) times min {γ₁−P_(*),P_(*)−γ₀} should probably be approximately 4 (somewhere between, say, 2and 10 is probably most desirable) times {square root}{square root over(P_(*)(1−P_(*))}. The marginal changes in the power supply might be oforder 0.01% of the current power supply level, but should not exceed aproportion of max {γ₁−P_(*), P_(*)−γ₀} in most embodiments. (As analternative or adjunct to adjusting the power supply, one could alsoadjust the length of the T1 detection period.) Note further thatwhenever the primary photon (quantum, etc.) emission surfaces are notelectrically activated, then their total emission rate probability needsto be made adjustable by some electromagnetic or electromechanical (orpossibly piezo-electric) means, which could involve something as simpleas varying the exposed area of such surfaces. Note that for any two realnumbers a and b with a≦b, min {a,b}=min{b,a}=a and max {a,b}=max{b,a}=b.

[0072] Fortunately, even though the laser's (or other photongenerator's) photon emission rate will not be perfectly constant, andneither will the detector's detection rate or pulse waveformdistribution, very nearly ideal random numbers can still be produced ifthe probability of no registered detection pulses changes very slowlyfrom one T1 time period to the next.

[0073] From our earlier analysis it is clear that this condition will besatisfied if the actual number of photons emitted by the laser does notchange by more than say, 1%, from one T1 time period to the next (withhigh probability). This condition will in turn be satisfied if thelaser's emission rate is periodic and cycles with sufficient rapidityrelative to T1 or if the laser's emission rate never drops too near tozero and simultaneously cycles sufficiently slowly relative to both T1and T1+T2+T3 time periods and if the photon (quantum) source is beingconstantly properly regulated.

[0074] From a sequence Y₁, Y₂, . . . , of ones and zeroes which areindependent (or nearly so) and are biased or have slowly changingprobability of being zero, one can select a subsequence which verynearly does meet quite rigid standards of providing essentiallyindependent identically distributed (i.i.d.) random numbers withessentially equal probability of ones and zeroes. The method, due toJohn von Neumann in 1951, is as follows:

[0075] Let Y₁, Y₂ . . . , denote the sequence of ones and zeroesproduced by the shift register (in one embodiment). Group the sequenceinto disjoint adjacent pairs (Y₁, Y₂), (Y₃, Y₄), . . . Eliminate allpairs with identical entries (0,0) or (1,1) and retain only the firstcomponent (or only the second component, or alternate which is retained,etc. More generally, retain exactly one of these two components based onany rule which makes its selection independently of the value of eithercomponent) of the other pairs. This gives a sequence X₁, X₂, . . . .which is a subsequence of the original {Y_(j)} sequence but which ismuch more nearly truly random because (for all j≧1),P((Y_(2j−1),Y_(2j))=(1,0)), the probability that Y_(2j−1) equals one andY_(2j) equals zero, is essentially equal to P((Y_(2j−1), Y_(2j))=(0,1)),the probability that Y_(2j−1) equals zero and Y_(2j) equals one. Sincethe {Y_(j)} are assumed to be essentially independent, the conditionalprobability that Y_(2j−1) equals (say) zero, given that Y_(2j−1)≠Y_(2j)and given Y₁, Y₂, . . . ., Y_(2(j−1)) is essentially equal toP(Y_(2j−1)=0, given Y_(2j−1)≠Y_(2j)), which is nearly one-half. Thus,even if the {Y_(j)} are inherently or recurrently biased toward one orzero, that bias is essentially absent in the {X_(k)} sequence.

[0076] One embodiment of the random number generator as described iscapable of producing about 43,000 random numbers per second, assumingthe von Neumann procedure is not used. Moreover, adjustments can easilybe made to increase the number of photons transmitted through theneutral density filters 14 by either increasing the power of the laseror by decreasing the net attenuation factor of the neutral densityfilters. Photomultiplier tubes are available which can produceregistered detection pulses based on detection of single photons perhapsas frequently as 100,000,000 per second or so if registered detectionpulses are short enough in duration. Dividing this number by In2, it maytherefore be possible to produce as many as 140,000,000 random numbersper second using the same basic configuration as shown in FIG. 1, withthe possible addition of a multiplexor, multiple deposition channels,etc. This rate of production is more than sufficient for all but themost demanding applications for random number generators using only asingle device 10. For scientific calculations or other applicationsdemanding billions of random numbers, several of the device 10 can becombined each of which is capable of producing as many as 140,000,000random numbers per second. In an alternative embodiment, an avalanchephoto diode is used which is capable of detecting in excess of 1 billionsingle photons per second with a flip flop(s), clock(s) and shiftregister (together with any other necessary electronics) capable ofrecording in excess of 1 billion values per second.

[0077] Because of its basic design and regulatory (and/or von Neumanndata analysis) components, the random number generator as described isless apt to be affected by changes in surrounding temperature and linevoltage than other physical random number generators, giving it astability allowing its use in a wide variety of applications.

[0078] In an alternative embodiment of the invention, the neutraldensity filters 14 are coordinated with the laser 12 to increase theaverage transmission of photons through the filters 14 by a factor often to the fifth power. This will result in about λ₀≡1.5×10¹⁰ photonsdeparting the attenuator per second (with a standard deviation of order{square root}{square root over (1.5)}×10⁵ photons). A photodetector isused which produces a registered detection pulse with probability p_(j)if j photons enter the detector during a time of 10⁻² seconds.

[0079] Let q_(j) denote the probability that j such photons enter thedetector during this time interval. Assuming that q_(j) approximatelysatisfies the Poisson probability law with parameter λ, q_(j)$q_{j} = {\left( {\exp \left( {- \lambda} \right)} \right){\frac{\lambda^{j}}{j!}\quad.}}$

[0080] The sum$Q \equiv {\sum\limits_{j = 1}^{\infty}\quad {q_{j}p_{j}}}$

[0081] describes the probability that a registered detection pulse willj=1 be produced during this time interval from a {q_(j)} photon arrivalprocess and a {p_(j)} detector process, as expressed in general form. Ifp_(j) is near one-half for, say, |j−λ|≦10{square root}{square root over(λ)}, Q will be very close to one-half. If the photo-detector is of morethreshold type, one might have, say,$p_{j} = {\frac{\left( {s_{j} + s_{j - 1}} \right)}{2},}$

[0082] where s₀=q₀ and, for j≦1, s_(j)=q₀+q₁+ . . . +q_(j). Then$Q = {{\sum\limits_{j = 1}^{\infty}\quad {\left( \frac{s_{j +}s_{j - 1}}{2} \right)\left( {s_{j} - s_{j - 1}} \right)}} = {{2^{- 1}{\sum\limits_{j = 1}^{\infty}\quad \left( {s_{j}^{2} - s_{j - 1}^{2}} \right)}} = {{2^{- 1}\left( {s_{\infty}^{2} - s_{0}^{2}} \right)} = {2^{- 1}{\left( {1 - s_{0}^{2}} \right)\quad.}}}}}$

[0083] Thus, by changing the q_(j) a little bit further one can make Qequal to one-half. Alternatively, by increasing the laser's rate ofphoton emission by a factor of (1−s₀ ²)⁻¹ (or adjusting the attenuator,etc.), Q can be made equal to one-half. For the example at hand, useλ=λ₀. Similarly to the one embodiment, if no registered detection pulseoccurs during the interval of length 10⁻² seconds (which is the settingof the T1 time period in this instance), a value of zero is assigned.Otherwise, a value of one is assigned. The assigned values are recordedin the shift register to produce a sequence of numbers (Y₁, Y₂, . . . ).Assuming that the laser's photon output over disjoint 10⁻² second timeintervals is essentially independent and of nearly constant order ofmagnitude, the {Y_(j)} will be an essentially i.i.d. sequence of onesand zeroes, with each Y_(j) having probability Q of being equal to one.When Q is not equal to (roughly) one-half, this can be corrected to(roughly) one-half by the von Neumann method.

[0084] If there are difficulties in allowing photo-detection to occurover an interval of time as long as, say, 10⁻² seconds, the detectionperiod could be restricted to a sub-interval of, say, 10^(−k) seconds.Alternatively or jointly, the laser could be designed to send pulses inshort i.i.d. bursts lasting about 10^(−k) seconds (for some k≧3) every10⁻² seconds.

[0085] However, it must be pointed out that random number generationbased on this kind of batched detection system may be much moresensitive to changes in line voltage and device temperature than thesingle photon detection scheme. Fluctuation in photon emission rateand/or registered detection rate due to these or other causes may makereliable production of long strings of nearly random stationary equallylikely binary bits difficult if not impossible to obtain or maintainwithout either reducing the number of photons in a batch orincorporating a sufficiently sensitive monitoring and regulatoryfeedback system to control the rate of photon emissions (which will havea minor impact on the degree of randomness achievable). As alluded toearlier, attenuation down to the single photon threshold detection casecircumvents this problem. It may also be circumvented, however, if thedetection probabilities p_(j) are (sufficiently) bounded away from zeroand one for, say, j between 0.9 λ and 1.1λ, as this would allow for aten percent fluctuation from the baseline photon emission (or quantumdetection) rate.

[0086] When operating in somewhat hostile environments (e.g., certaincomputers, outer space, etc.), it may be necessary or desirable toshield the random number generator photonically, thermally,electro-magnetically, or from X-rays, gamma rays, cosmic rays, ions,etc. Conversely, it may be necessary to shield surrounding electronic orother equipment, devices, or people from the random number generator.

[0087] Moreover, it may also be desirable to make various components ofthe system utilizing compounds of zirconium tungstate, or the like, toensure that key parts do not significantly vary in size as temperatureschange due to use or environmental factors.

[0088] Black Body Sources

[0089] As opposed to a laser light source, which has the property thatit emits a highly collimated beam of essentially monochromatic light(i.e., photons of a single wavelength), one could also generate photonsby a thermally controlled black-body type source. To do so, one coulduse a DC (direct current) power source equipped with a power supply(self-)controller to heat a vacuum enclosed tungsten filament, using thetungsten as a resistor in an electrical circuit in one embodiment, andmaintain it at an approximately constant chosen temperature. Thetungsten will approximate a black body cavity resonator, emittingphotons of virtually all wavelengths from its surface at a rate roughlyproportional to the black body rate with a tungsten specificcharacteristic proportionality constant which depends principally ontemperature and wavelength. For each photon wavelength λ>0 and eachabsolute temperature T (measured in degrees Kelvin), the photon emissionrate density at equilibrium is presumably a constant r(λ,T) per unitsurface area. One could potentially increase the number of photonsemitted per second from a given piece of tungsten of a given temperatureby drilling holes part-way into it (which may increase the rate of highenergy photons emitted to an even greater degree, as the interior of thetungsten may be hotter than the exterior) or by otherwise increasing itseffective surface area (such as by creating a long, stringy coiledfilament, as is commonly done in a light bulb).

[0090] Tungsten is a good choice of material for an approximate blackbody photon source because of its high melting point (about 3410°Centigrade).

[0091] By varying its temperature between, say, 300° K and 1500° K, anappropriate sized piece of tungsten or tungsten filament should be ableto produce a range of registered detection pulses which would certainlyinclude the interval [10,10⁹] based on photon emissions having, say,wavelengths less than or equal to, say, 632.8 nanometers, without theneed of an attenuator. (With corresponding changes in temperaturerequirements, other wavelength intervals could produce such detectionrates.) Moreover, a prism could be used (not only as a flat piece ofglass but also) as a mechanism for selecting the photons with, forexample, shorter wavelengths. More simply, a color filter or tintedglass could be used to select for certain families of wavelengths.Shorter wavelengths could also be produced via a nonlinear opticalcrystal which induced second harmonic generation.

[0092] Per unit time per unit area photon emission rates from an idealblack body source from various collections of wavelengths can becalculated based on the energy E_(λ) of a photon of wavelength λ (recallthat $E_{\lambda} = \frac{hc}{\lambda}$

[0093] applied to Planck's radiation formula for black body (cavity)radiation:$R_{\lambda} = {\frac{C_{1}}{\lambda^{5}}{\left( \frac{1}{{- 1} + {\exp \left( {{C_{2}/\lambda}\quad T} \right)}} \right)\quad.}}$

[0094] Here h is Planck's constant, λ is the wavelength of a givenphoton, T is the temperature in degrees Kelvin, C₁=2πc²h, c is the speedof light, C₂=hc/k, k is Boltzman's constant, and R_(λ) (known as thespectral radiancy) is the radiation density per square centimeter due tophoton emissions of wavelength λ. For temperatures T in the range ofroughly 500°-1400° K, an increase in Kelvin temperature by around 25° atthe low end and 200° or so at the high end is required to increase thephoton output (for a black body) of wavelengths at or below about 600nanometers by a factor of ten. Therefore, for the tungsten source, itshould be clear that the temperature required to produce photon outputsin the [10,10⁹] range can be readily calibrated. Furthermore, it shouldnot be hard to maintain.

[0095] The heated tungsten would normally be installed in an evacuatedtransparent or tinted glass (or possibly heat proof plastic or othermaterial) housing and located outside or even inside the detector.However, if it proved feasible or advantageous to generate randomnumbers from thermionic emission of electrons (with or without theconcommitant use of photons), then it might be desirable to locate thetungsten (or other heating element) without its housing, but probablycoated with some appropriate dielectric or semi-dielectric material ofsuitable thickness, inside the detector (such as inside the firstchamber of a PMT (photomultiplier tube), or an EMT (electron multipliertube), closed off from the external environment), assuming its heatand/or presence would not interfere with the functioning of the PMT orother detector. (Of course, the PMT could be cooled).

[0096] Because of the already present electric fields inside a PMT (orEMT), random number generation based on thermionic emission of electronswould seem to consume (much) less power (i.e., require lower tungsten(or other heating element) temperatures) at a given random numbergeneration rate than one based on the photon emissions of the same pieceof tungsten placed in an electron absorbing housing.

[0097] Ignoring its possible benefits as an electron source, a (variablemagnitude) direct current powered tungsten light source provides anumber of general benefits over the laser as a photon source for thepurpose of generating random numbers (bits). For instance, there is noneed for attenuation of photons because one generates only the amountneeded. This will reduce cost, complexity, and the level of heatgeneration. Also, there is less need of precision alignment betweenlight source and detector since the tungsten will radiate photons(and/or electrons) in a multitude of directions. Therefore, the photongenerator does not need to be in such a rigidly exact alignment withrespect to either the detector or any system of attenuation, as requiredby a laser. Furthermore, by employing a less collimated photon source,the detector should age more slowly because its plates would experiencemore extensive and uniform regions of use, greatly reducing consumerreplacement cost.

[0098] Moreover, since photons of lower wavelength have more energy,they will typically produce detector pulses of greater amplitude. Thisopens the door to generating random bits at a higher rate from ablack-body type photon source such as tungsten than a laser photonsource since the laser produces a narrower distribution of amplitudesamong the outputted detection pulses than a black body type source. Thesimplest way of accomplishing an improved random bit generation ratewould be to select an integer k+1 and split the amplitude heights of theregistered detection pulses into k disjoint categories, possiblyallowing for an additional “no registered pulse” category. Ideally, thecategories might be chosen so that a random registered detection pulseis (roughly) equally likely to belong to each of the categories.Categories consisting of single non-overlapping intervals can beconstructed to (approximately) achieve this goal. In general, the widthsof the intervals will be different from one another and requireadjustment as the temperature of the tungsten or other black body typephoton source changes. If one wants to use disjoint categories C₁, C₂, .. . , C_(k) of amplitudes of registered detection pulses for which boththe average number of photons detected and the average energy of theimputed number of photon emissions from the tungsten (or whatever otherblack body type photon source is used) does not vary (to the relevantdegree of approximation) from category to category, it should bepossible to achieve this goal by means of 2k−1 disjoint intervalsI_(k)<I_(k−1)< . . . <I₂<I₁<J₂<J₃< . . . <J_(k) and categories of theform C₁=I₁ and, for 2≦j≦k, C_(j)=I_(j)∪J_(j). (Given two intervals A andB of reals, A<B means that every real number belonging to the set A isless than every real number belonging to B.) Because the photon streamemitted by the black-body type source is a Levy process, the registereddetection pulses of each of the k separate amplitude categoriesconstitute independent (roughly) Poisson processes (ignoring the deadtime of the detector and the pulse widths). Therefore, by recording theamplitudes of successive registered detection pulses, separating theminto k categories, possibly allowing for an additional “no registeredpulse” category, generating random bits based on the category assignedand its Poisson-governed arrival times, more bits can be generated thanif one merely lumped all detection pulses into a single category,thereby ignoring (except for the possible requirement that all theamplitudes exceed some defined and chosen threshold or belong to someinterval) variations in their amplitude. By also keeping track of thearrival times, pulse height durations and/or oscillations, etc., evenhigher random bit rates can be achieved.

[0099] It should be possible to identify pulse waveforms typical of“dark counts” so as to define the notion of a registered detection pulseso as to exclude possibly the vast majority of these frequently unwantedsignals, possibly primarily retaining only those whose probabilitydistribution is governed by an independent Poisson or Levy process.

[0100]FIG. 2 illustrates one embodiment of a random number generatorhaving a black-body type of photon source. Referring to FIG. 2, atungsten black body type light source is shown coupled to aphotomultiplier tube. An optional prism, filter or tinted glass may becoupled between the black body light source and the photomultipliertube. In order to avoid obscuring the invention, a DC power supply,electronics of the recording system and the monitoring system have notbeen shown.

[0101] Use of Dark Counts as a Source of Random Registered DetectionPulses

[0102] The electrical current output and waveform of a photomultipliertube (or other quantum phenomena detector) will be affected not only bythe photons or other quantum phenomena intentionally sent into it, butmay also be affected by the detector itself, with its electronic andmolecular processes (quantum and otherwise) acting inside it, togetherwith the intrusion of various external events such as cosmic rays andinternal or ambient temperature. The current output from unintendedsources (as typically measured by sealing off photonic entry to the PMT)is referred to as “dark current”.

[0103] Generally, there are about six categories of causes of so-calleddark counts (or dark current) within a photomultiplier tube (includingthermionic emission of electrons, leakage current, glass scintillation,field emission current, ionization current due to residual gases, andother noise current). To a substantial degree, restricting theregistered detection counts to pulses of some minimum amplitude or someinterval of amplitudes and/or amplitude interval durations, etc., basedon the photon wavelength distribution (or quantum event distribution)from the light source (or quantum event generator) may restrict the rateat which registered detector pulses derive from the dark counts.Moreover, to the extent to which such amplitude and/or waveformconstraints permit the receipt of dark counts which constitute a Poissonor Levy process which is independent of the (presumably) inputted photon(quantum) process, the dark counts themselves may contributeconstructively to the generation of random numbers (bits). In fact, ifthe rate of production of random numbers from dark counts is high enoughfor the needs, and considered suitably random, no input photons or otherquantum phenomena would be necessary, since all the random numbers couldbe generated from dark counts. Closing off the PMT (or other detector)photonically and possibly removing or replacing the photocathode plate,as discussed momentarily, one could readily generate about 1000registered detection pulses per second from dark counts, with anappropriate choice of a PMT. At room and surrounding temperatures, theprobability of electron emission per unit surface area varies amongdifferent materials over a huge range encompassing very many orders ofmagnitude (copper and silver being near the high end, silicon being nearthe middle, and fused quartz and diamond at the bottom). As a result,and considering the electric fields present, a grounded conducting plateof suitable surface area with a thin coat of suitable composite materialcan be constructed to provide thermionic electron emission at ambienttemperatures at virtually any fixed desired rate from one to 10⁹ countsper second when located strategically in the first chamber of a(possibly somewhat modified) PMT or EMT (or other detector).

[0104] Somewhat less desirably, the number of such dark counts, andhence the number of registered detection pulses derived therefrom, couldalso be increased by heating part or all of the initial chamber of thePMT (or other detector) (such as by introducing a possibly coatedtungsten or nichrome wire segment or other heating element at astrategic location in this region).

[0105] Perhaps more favorably, one might introduce into the firstchamber a grounded, partially exposed, sharp metal object such as aneedle (or possibly many needles, even an entire array). In the presenceof a positive electric field on the first (dynode) plate, electronswould presumably be pulled off a nearby needle tip at Poisson rate. Thisrate would depend on various aspects, such as the needle's metalliccomposition, its thickness, its sharpness of tip, any coating, itscomposition and thickness, temperature and electric field near the tip(as governed by things such as the voltage on the first plate, theplate's size, the needle tip's distance from it, etc.). Ideally, thiswould produce registered detection pulses at the desired rate. If,however, too many electrons were emitted by the needle per second, therate could be reduced to virtually any desired amount by coating theneedle with an appropriate material (pure or composite) of suitablethickness (thinness) and electron emission probability. Also, if therate of electron emission needed to be increased, a suitable (roughly)constant negative voltage (monitored and regulated) could be applied tothe needle. (Less desirably, more needles could be added.) The resultantlarge negative electric field near the tip of the needle would then alsorapidly accelerate the speed of any electron it emitted, thereby(possibly greatly) increasing the number of secondary recoil electronsproduced when such an initial electron impacts the first PMT (or EMT, orother detector) plate (which is now a positively charged dynode platerather than a photocathode plate). The monitoring and regulation of sucha voltage or other power supply could be based on the number of onesproduced by the detector among the last n_(*) bits, as described morefully earlier. Moreover, because gold is so good at uniformly diffusingheat, as well as conducting electricity, it might be desirable tosputter a thin gold film (or possibly silver, in some embodiments) onthe (perhaps, but not limited to, iron, steel, copper, brass, tungsten,nickel, chromium, or some alloy thereof) needle tip, whether or not a(relatively) electron emission inhibiting coating is also then used.

[0106] Presumably, the choice of metallic composition of the needle andany coating would be affected by the temperatures generated at its tip,as well as the anticipated internal and external electric fields thereinand nearby, together with the desired rate of electron emission.

[0107] If the polarity on the needle tip is (sufficiently) reversed(i.e., made sufficiently positive), the intense field at the tip of theneedle could strip off one or more electrons of any hydrogen, helium,nitrogen or possibly any other gas, atom or molecule present inside thephotomultiplier tube (or other detector) which happened to hit theneedle tip or happened to arrive in sufficient proximity thereto. Thepositive ion so formed would then be repelled by the needle and itssurrounding positive electric field and be accelerated toward the firstplate (normally called a dynode) inside the PMT or other detector. Bymaking its voltage negative, this plate could contribute to theacceleration of the positive (preferably helium or nitrogen) ion. Asusual, all subsequent dynode plates would be set at positive andsuccessively higher voltages in order to accelerate the successivelyproduced free electrons toward the successive dynode plates. Regardingany photocathode or negatively charged plate as the first plate and thefirst positively charged dynode plate as the second plate, the possiblevirtue of this design over the photon detection designs discussedpreviously is that whereas there is typically only about one (on theaverage, its a fraction) electron produced at the first (photocathode)plate, in this instance there would be some number n, where n depends onthe energy with which the positive ion, which then becomes neutralized,hits that plate. Consequently, the amplitudes of the current from thelast plate would also be multiplied by an average factor of n. Moreover,because the subsequent dynode plates are all increasingly positivelycharged, the introduction of a positively charged needle(s) followed bya negatively charged first plate need not increase the maximum appliedvoltage's deviation from zero.

[0108]FIG. 3 illustrates one embodiment of a random number generatorthat uses thermionic emission of electrons. Referring to FIG. 3, aphotomultiplier tube has a closed off face plate. The photomultipliertube also includes a properly grounded conductor coated with material ofappropriate electron emission probability located at the point near theclosed off end of the tube or closer to the dynodes. Again, the DC powersupply, electronics of the recording system and monitoring system arenot shown to avoid obscuring the present invention.

[0109]FIG. 4 illustrates one embodiment of a random number generatorhaving electron emission from a needle. Referring to FIG. 4, aphotomultiplier tube with a closed off face plate is shown. A groundedand suitably coated needle, possibly at a constant negative voltage, islocated inside the photomultiplier tube at a suitably chosen distancefrom the first dynode plate. Again, the DC power supply, electronics ofthe recording system and the monitoring system have not been shown toavoid obscuring the present invention.

[0110] By controlling the amount of helium, nitrogen, and other gasesinside the modified PMT (or other detector) and/or the number of needles(more (positively charged) needles are advantageous in this case and cancompensate for fewer gas molecules) and their tip sizes, one couldcontrol the rate at which the movements of the electrically neutral,uncharged gases (often modeled as driftless homogeneous Brownian motionprocesses) would cause them to hit the needle tip(s), thereby producingwhat should be a highly random succession of output pulses, withoutaffecting the performance of the dynode plates, relying as they do on ahighly evacuated environment. Moreover, since the modified PMT or EMT(or other detector) is to be closed off, it can be housed in anothercontainer so that it need not be subject to the entry of helium gasdiffusing from the outside air in through the glass and into theinterior of the detector. By controlling the size of the needle tips,their positive voltages, and the (negative) voltage on the first plate,perhaps it would be possible to make n, the number of recoil electronsfrom the first (negatively charged) plate, as large as 100 or 1000 ormore, in which case the electronics of random number generation would becapable of greater speed, simplification and/or safety, as either fewerfurther pulse amplification steps would be necessary or lower maximumPMT voltages could be used.

[0111] By selecting appropriate materials of an appropriate size (andthin-ness), suitably well grounded, on or near or in place of thephotocathode plate, one could theoretically produce random bits viathermionic emission of electrons at room temperature (and/or a broadinterval of surrounding temperatures) from a relatively smooth surfaceat rates at least as high as 10⁹ per second (if the detector couldhandle such a rate) without the need of attenuation. If there were somequestion about slight correlations of temporally nearby electronemissions, one could consider only those pulses which occurred at leastto time units after the last recognized detector pulse. In manyembodiments, it is anticipated that 0≦t₀≦10⁻⁶ sec. Since the temperatureat which the device operates may change from use to use or even duringuse, the von Neumann technique might be used. Otherwise one may need touse a monitoring system to actively monitor and readjust for changingrates of electron emission, possibly cooling (or heating) the detector,changing voltages, etc.

[0112]FIG. 5 illustrates one embodiment of random number generator thatoperates based on movements of gas molecules. Referring to FIG. 5, aphotomultiplier tube is shown with a closed off face plate and ispowered by a DC power supply. One or more needles are shown held at aconstant positive voltage. The electron multiplier (the dynodes) areheld at successively higher charges. The first of the dynode plates isnegatively charged.

[0113] With respect to detectors in general, many types of detectors toobtain registered detector (or detection) pulse may be used. In oneembodiment, the purpose of generating random bits (or random numbers),all that is required is that there results in the detector itself a(roughly) independent and identically distributed (i.i.d.) sufficientlynon-constant random process.

[0114] Thereby, (roughly) i.i.d. registered detection pulses willsometimes occur, and sometimes not occur. Furthermore, if suchregistered pulses are sufficiently different sufficiently often, theirwaveforms can be used to produce random bits at higher rates bysplitting such pulses into k+1 mutually disjoint categories, C0, C1 . .. , Ck and outputting a distinct symbol for each category. (Category COis used to denote the “no registered detection pulse” category.) Suchcategories can be constructed based on pulse height alone, pulseduration alone, their joint behavior, or even progressively finer pulseshapes. The reason this observation is so liberating is that for eachelectronic device in each age of its technological advancement there isa natural order of magnitude of charge and/or voltage used in itstypical circuitry. Therefore, it should often prove possible to selectthe i.i.d. random process to be monitored or the method of so doing tonaturally and “automatically” produce detection pulses of just thatappropriate order of magnitude, thereby not requiring major reprocessingor amplifying of the signals (electronic or otherwise) from the detectorto inject random bits into the system. With this idea in mind, it shouldnot be necessary to only send and detect single photons, etc. Largenumbers of photons or other quantum phenomena could be repeatedly sentinto any detector capable of converting them to nonconstant (roughly)i.i.d. random pulses. Random bits could then be produced therefrom aslong as the detection pulse waveforms they produce are sufficientlydifferent sufficiently often.

[0115] Random bits and random numbers can be sensibly produced in manyadditional ways. Several a listed below and very briefly discussed, eachrelated in part to application of Heisenberg uncertainty principle.

[0116] One method involves using sufficiently collimated x-rays sentpreferably roughly one by one into a crystalline atomic structure, suchas salt (NaCl), at an appropriate angle to the molecular lattice todiffract off at a sequence of lesser principle angles according to asuccession of decreasing probabilities. One or more detectors could beset up along such respective paths, producing bits based on receipt ornon-receipt of a so-called registered detection pulse from a (so-calledT1) detection interval of calibrated, possibly adjustable, length. As arefinement, one could gait the x-rays, keeping track of the analog ordigitized time elapsed from the start of such a so-called T1 detectioninterval until first receipt of a registered pulse.

[0117] Even if the x-rays are being produced and sent into the crystalat a faster rate than desired, one can compensate for this by setting upthe detector(s) along sufficiently low probability paths. Hence, nospecial attentuator is required as the detection angle automaticallyperforms the needed attenuation.

[0118] Moreover, since x-rays posses much greater energies than visiblelight, they should prove to be much less expensive to detect. On theother hand, if used near humans, a random number generator based onx-ray production and detection might necessitate shielding.

[0119] Another method is analogous to the first except that electronsare to be used, and the crystal lattice might be of, say, nickel. Thisdevice might require electromagnetic shielding from external fields.However, it would have the advantage of being operable over a very broadrange of energy levels, making it somewhere between possible and quitelikely that the optimal choice of electron energy for the application athand would be generally desirable and competitive.

[0120] In another method, sufficiently collimated photons can also bediffracted by (and around) a one-sided boundary. Thus, if an opaqueplanar object having a straight, sharp edge (such as a razor blade) isslowly moved transversely into the path of a laser beam, it will bothdiffract and attenuate it. Once initially adjusted, the light-blockingblade could be positioned and re-positioned by a piezo-electric or otherelectromechanical device, with the apparent modifications, the conceptsand approach mentioned in first method also apply to this method.

[0121] Still, another method is possible because recently has becomepossible to cool atoms down to within a few billionths of a degreekelvin. An object so close to absolute zero in temperature has aposition (as defined by, say, its center of mass) which is known withgreat precision. By the Heisenberg certainty principle, its momentumthen possess a certain corresponding degree of uncertainty. As a result,the object begins to move in apparently random directions. By sensingand recording such (at least somewhat) random changes in direction (orrather, in momentum), it should be possible to produce random numbers ofrandom bits. The more exactly the change in momentum can be recorded,the more random bits can be generated at once.

[0122] There have been thus described preferred and alternativeembodiments of a random number generator. While preferred embodimentshave been described and disclosed, it will be recognized by those withskill in the art that modifications are within the true spirit and scopeof the invention. The appended claims are intended to cover suchmodifications.

1. A random number generator comprising: a black body source forgenerating quantum phenomena; a photodetector coupled to receive thequantum phenomena; and a recording system coupled to receive indicationsof detections made by the detector.
 2. The apparatus defined in claim 1wherein the detector comprises a photomultiplier tube.
 3. The apparatusdefined in claim 1 further comprising a direct current (DC) generatorcoupled to the black body source.
 4. The apparatus defined in claim 1wherein the black body source comprises a tungsten filament.
 5. Theapparatus defined in claim 1 further comprising a monitoring system thata monitors bit production rate.
 6. The apparatus defined in claim 1wherein the recording system includes: a multiplexor to receive theoutput of the detector; a plurality of channels coupled to the outputsof the multiplexor; and a demultiplexor with inputs coupled to thechannels and an output, wherein the multiplexor and demultiplexor arecontrolled to cyclically receive outputs of the detector and generate asingle output string.
 7. The apparatus defined in claim 1 furthercomprising a color filter to restrict the photons entering the detectorinto a desired interval.
 8. The apparatus defined in claim 1 furthercomprising a tinted glass to restrict the photons entering into adesired interval.
 9. The apparatus defined in claim 7 wherein the colorfilter is located inside the detector.
 10. The apparatus defined inclaim 8 wherein the color filter is located inside the detector.
 11. Theapparatus defined in claim 4 wherein the temperature of the filament isadjusted to produce photons at a desired rate.
 12. The apparatus definedin claim 11 wherein the tungsten acts as a resistor to create heat whenthe direct current is supplied thereto.
 13. A random number generatorcomprising: a detector having a needle position within the detector togenerate electrons, the detector detecting the electrons; and, arecording system coupled to the detector.
 14. The apparatus defined inclaim 13 wherein the needle comprises an electrically grounded needle.15. The apparatus defined in claim 14 wherein the electrically groundedneedle is coated with a dielectric.
 16. The apparatus defined in claim14 wherein the electrically grounded needle is coated with a materialhaving a selected electron emission probability.
 17. The apparatusdefined in claim 13 wherein the needle comprises a negatively chargedneedle.
 18. The apparatus defined in claim 17 wherein the negativelycharged needle is held at a constant voltage.
 19. A random numbergenerator comprising: a detector having a closed off detector containingmaterial with thermionic emission capabilities, the detector detectingemitted electrons; and a recording system coupled to the detector.